Answer: The LP model is given as :
max: 1.180( 420000 A + 500000 B )
subject to : (a.) 7000 A + 2500 B ≤ 100000
(b.) 7000 A ≤ 70000
(c.) 2500 B ≤ 50000
Explanation:
Let us assume;
A be the no. of T.V spots
B be the no. of magazine spots
Given:
(a.) Mountain Mist earns a profit margin of $1.80 on each case of soda that it sells.
(b.) Each TV spot costs $7000 and is expected to increase sales by 420,000 cases.
(c.) Each magazine ad costs $2500 and is expected to increase sales by 500,000 cases.
∴ The objective function of this model will be given as :
max: 1.180( 420000 A + 500000 B )
(d.) A total of $100,000 may be spent on TV and magazine ads combined.
(e.) Mountain mist wants to spend no more than $70,000 on TV spots and no more than $50,000 on magazine ads.
∴ The subjective function will be :
(a.) 7000 A + 2500 B ≤ 100000
(b.) 7000 A ≤ 70000
(c.) 2500 B ≤ 50000
∴ The LP model is given as :
max: 1.180( 420000 A + 500000 B )
subject to : (a.) 7000 A + 2500 B ≤ 100000
(b.) 7000 A ≤ 70000
(c.) 2500 B ≤ 50000
